Related papers: Acyclic Gambling Games

For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…

We consider zero-sum stochastic differential games with possibly path-dependent controlled state. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback…

In this paper we consider two-person zero-sum risk-sensitive stochastic dynamic games with Borel state and action spaces and bounded reward. The term risk-sensitive refers to the fact that instead of the usual risk neutral optimization…

Consider a two-player game repeated N times. Player 1 can choose between two styles (for interpretability, offensive and defensive), whereas Player 2 uses a single fixed style. Let X N\,:= \#wins -\#losses for Player 1 after N games, and…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

We consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

We study two classes of zero-sum stochastic games with compact action sets and a finite product state space. These two classes assume a communication property on the state spaces of the players. For strongly communicating on one side games,…

This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates…

We generalize the results of Fleming and Souganidis (1989) on zero sum stochastic differential games to the case when the controls are unbounded. We do this by proving a dynamic programming principle using a covering argument instead of…

This paper provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and…

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

We study $\lambda$-discounted zero-sum games as the discount factor $\lambda$ approaches $0$ (that is, the players are more and more patient), in the context of games with stage duration. In stochastic games with stage duration $h$, players…

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the…

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing…

In this paper we study a two person zero sum stochastic differential game in weak formulation. Unlike standard literature which uses strategy type of controls, the weak formulation allows us to consider the game with control against…

Zero sum games with risk-sensitive cost criterion are considered with underlying dynamics being given by controlled stochastic differential equations. Under the assumption of geometric stability on the dynamics , we completely characterize…

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his…

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

Two-player, turn-based, stochastic games with reachability conditions are considered, where the maximizer has no information (he is blind) and is restricted to deterministic strategies whereas the minimizer is perfectly informed. We ask the…